Two quantities that are often useful are the overlaps of its evolved form \(|{\bf z} (t)\rangle \)  with some coherent state bra vector, \(\langle {\bf z}^\prime | {\bf z} (t)\rangle \)  (coherent state path integral matrix element), or projection onto quadrature variable bra vector eigenstates, \(\langle {\bf x} | {\bf z} (t)\rangle \) . The saddle point approximation of either of these quantities results in a multiplication of the inverse square root of complex valued determinants. Using quadratures, these quantities can be made to look identical to forms arising with Gaussian wave packets [1]} whose determinants are given ahead. One discussion of the parameter mapping between them can be found in Appendix A of [2]}. Roughly speaking, the complex parameters of \({\bf z}\)  can be mapped onto pseudo-momentum and -position centroids, and the ground state links the shape parameters.
